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Physics
Chemistry
Maths
(i) Why do the 'free electrons', in a metal wire, 'flowing by themselves', not cause any current flow in the wire ?
Define 'drift velocity' and obtain an expression for the current flowing in a wire, in terms of the 'drift velocity' of the free electrons.
(ii) Use the above expression to show that the 'resistivity', of the material of a wire, is inversely proportional to the 'relaxation time' for the 'free electrons' in the metal.
A 100 V battery is connected to the electric network as shown. If the power consumed in the 2 Ω resistor is 200 W, determine the power dissipated in the 5 Ω resistor.
(i) Derive an expression for drift velocity of electrons in a conductor. Hence deduce Ohm’s law.
(ii) A wire whose cross-sectional area is increasing linearly from its one end to the other, is connected across a battery of V volts. Which of the following quantities remain constant in the wire ?
(a) drift speed
(b) current density
(c) electric current
(d) electric field
Justify your answer.
In the two electric circuits shown in the figure, determine the readings of ideal ammeter (A) and the ideal voltmeter (V).
The potential difference across a resistor ‘r’ carrying current ‘I’ is Ir.
(i) Now if the potential difference across ‘r’ is measured using a voltmeter of resistance ‘’, show that the reading of voltmeter is less than the true value.
(ii) Find the percentage error in measuring the potential difference by a voltmeter.
(iii) At what value of ’, does the voltmeter measures the true potential difference?
What is meant by rate of a reaction ? Differentiate between average rate and instantaneous rate of a reaction.
Following reactions can occur at cathode during the electrolysis of aqueous silver nitrate solution using Pt electrodes:
In a galvanic cell, the following cell reactions occurs:
E°cell = +1.56 V
(i) Is the direction of flow of electrons from zinc to silver or silver to zinc?
(ii) How will concentration of Zn²⁺ ions and Ag⁺ ions be affected when the cell functions?
(i) Following reactions occur at cathode during the electrolysis of aqueous silver chloride solution :
= +0.80 V
= 0.00 V
On the basis of their standard reduction electrode potential (E°) values, which reaction is feasible at the cathode and why ?
(ii) Define limiting molar conductivity. Why conductivity of an electrolyte solution decreases with the decrease in concentration ?
When a certain conductance cell was filled with 0.1 M KCl, it has a resistance of 85 ohm at 25°C. When the same cell was filled with an aqueous solution of 0.052 M unknown electrolyte, the resistance was 96 ohms. Calculate the molar conductance of the electrolyte at this concentration.
[Specific conductance of 0.1 M KCl = 1.29 × 10⁻² ohm⁻¹ cm⁻¹]
If the function f : R → R is given by f(x) = x² + 3x + 1 and g : R → R is given by g(x) = 2x – 3, then find
(i) fog (ii) gof
If the function f : R → R is given by f(x) = and g : R → R is given by g(x) = 2x – 3, then find
(i) fog (ii) gof
Is f⁻¹ = g?
If the function f : R → R be defined by f(x) = 2x – 3 and g : R → R by g(x) = x³ + 5, then find fog and show that fog is invertible. Also, find (fog)⁻¹, hence find (fog)⁻¹(9).
Let f : N → R be a function defined as f(x) = 4x² + 12x + 15. Then show that f : N → S, where S is range of f, is invertible. Also find the inverse of f.
If f(x) = then Show that fof(x) = x for all What is the inverse of f?